Is it normal that my boyfriend thinks I will cheat on him 1day

In general it's probably not normal but for a person who's been hurt before by a cheating partner it's somewhat normal. Also if someone has a very low self esteem and maybe even a bit of an inferiority complex.

Regardless, if you're not actually cheating or engaging in behaviors that could lead to cheating it's your partner's issue not yours. Beware if your significant other is excessively jealous, controlling and tries to cut you off from family and friends. Even if the person has been hurt by other's infidelity in the past it's NEVER an excuse for any kind of abuse.

Take your time and don't be in a rush to get married before this issue is resolved.